|WikiProject Mathematics||(Rated Start-class, Low-importance)|
We can definitely expand the section on Brill-Noether theory to include some concrete statements as well as adding some references (viz. ACGH).
are particular, in the sense of determining more compatible functions than would be predicted.
On the page it says:
There is a lower bound ρ for the dimension dim(n, r, g) of this subscheme in Pic(C): dim(n, r, g) ≥ ρ = r(n − r + 1) − (r − 1)g
This cannot be right. Pic(C) has dimension g so defenitly the left hand side is smaller then g. However the right hand side can defenitly be largen then g by taking n large enough! I don't know bril noether theory so I don't know how to fix it but I suspect that "this subscheme in Pic(C)" should instead be a subscheme of C^n or maybe the nth symmetric power of C.